System for complex impedance measurement

Abstract

A measurement system is provided for measuring a complex transfer function of a system under test. The measurement system comprises a signal source for generating an input signal to be applied to the system under test, a signal detection device for detecting a response signal of the system under test in response to the input signal; and a signal analyzing system for determining the gain and phase shift of the system under test by comparing the response signal to the input signal. The signal analyzing system includes phase adjustment means to adjust a relative phase difference of the detected response signal and input signal; and curve fitting means to identify a phase difference adjustment of the phase adjustment means which gives the best fit of the response signal to the input signal. The phase measurement of the response signal is determined from the best fit phase difference adjustment.

The invention claimed is: 
     
       1. A measurement system for measuring a complex transfer function of a system under test, the measurement system comprising:
 a signal source for generating an input signal to be applied to the system under test; 
 a signal detection device for detecting a response signal of the system under test in response to the input signal; and 
 a signal analyzing system for determining the gain and phase shift of the system under test by comparing the response signal to the input signal, 
 the signal analyzing system including: 
 phase adjustment means to perform a relative shift of the detected response signal and input signal along a time axis to adjust a relative phase difference therebetween; and 
 curve fitting means to identify a phase difference adjustment of the phase adjustment means which gives the best fit of the response signal to the input signal, wherein the phase measurement of the response signal is determined from the best fit phase difference adjustment. 
 
     
     
       2. The measurement system of  claim 1 , wherein the curve fitting means further comprises identifying means to identify an amplitude difference between the response signal and the input signal and gain adjustment means responsive to the identifying means to match the amplitudes of the response and input signals. 
     
     
       3. The measurement system of  claim 2 , wherein the curve fitting means identifies an amplitude adjustment which gives a best fit of the detected response signal to the input signal, and wherein the gain measurement of the response signal is determined from the amplitude adjustment giving the best fit, the curve fitting for phase and gain determination being performed in concert to obtain the best fit of the detected response signal to the input waveform. 
     
     
       4. The measurement system as claimed in  claims 3 , wherein the signal source includes an electronic memory and the input signal waveform is defined digitally and stored in the electronic memory, the signal source being arranged to generate an input signal having an arbitrary waveform. 
     
     
       5. The measurement system of  claim 4 , wherein the arbitrary waveform is defined by a single sinusoidal waveform or a plurality of superimposed sinusoidal waveforms. 
     
     
       6. The measurement system of  claim 4 , wherein the arbitrary waveform is periodic. 
     
     
       7. The measurement system of  claim 4 , wherein the stored waveform includes at least a portion of a full cycle of the arbitrary waveform from which a full cycle of the waveform can be reconstituted. 
     
     
       8. The measurement system of  claim 4 , wherein the stored waveform includes a plurality of cycles of the arbitrary waveform. 
     
     
       9. The measurement system as claimed in  claim 1 , wherein the signal analyzing system includes a feedback path which feeds back the response signal, the fed back response signal being used to adjust the gain and offset of the input signal to produce a response signal approaching a maximum amplitude and minimum offset without clipping of the response signal and to provide compensation for errors introduced by the spectral phase and pain response of amplifiers, ADCs and other circuitry in the measurement system. 
     
     
       10. A method of measuring a complex transfer function of a system, the method comprising:
 generating an input signal to be applied to a system under test; 
 detecting a response signal of the system under test in response to the input signal; 
 determining the gain and phase shift of the system by comparing the response signal to the input signal, the comparison including: 
 adjusting a relative phase difference of the detected response signal and input signal by performing a relative shift of the signals on a time axis; and 
 curve fitting the phase adjusted signals to identify a phase difference adjustment which gives the best fit of the input signal to the response signal, wherein the phase measurement of the response signal is determined from the best fit phase difference adjustment. 
 
     
     
       11. The method of  claim 10 , further comprising relatively adjusting amplitudes of the response signal and input signal; and
 curve fitting the amplitude adjusted signals to identify an amplitude adjustment which gives the best fit of the input signal to the response signal, wherein the gain measurement of the response signal is determined from the best fit amplitude adjustment, the curve fitting for phase and gain determination being performed in concert to obtain the best fit to the input waveform. 
 
     
     
       12. The method of  claim 10 , wherein the signal source generates an input signal having an arbitrary waveform. 
     
     
       13. The method of  claim 12 , wherein the arbitrary waveform is defined by a single sinusoidal waveform or a plurality of superimposed sinusoidal waveforms. 
     
     
       14. The method of  claim 13  wherein the arbitrary waveform is periodic and the stored waveform includes at least a portion of one full cycle from which a full cycle of the arbitrary waveform can be reconstituted. 
     
     
       15. The method of  claim 13  wherein the arbitrary waveform is periodic and the stored waveform includes at least one full cycle of the arbitrary waveform. 
     
     
       16. The method as claimed in  claims 10 , wherein the input signal is also applied to a reference system the dynamic properties of which are known. 
     
     
       17. The method as claimed in  claims 10 , wherein the response signal comprises a response component and a background component and by comparing the response signal to the input signal the signal analyzing system identifies the background component from the response component while determining the gain and phase shift of the system. 
     
     
       18. The method of  claim 17 , wherein the response component of the response signal of the system under test is compared to a response of the reference system to compensate for artefacts of the measurement system or the transducers used to interface to the system under test. 
     
     
       19. The method of  claim 10 , wherein the signal detection device samples the response signal in response to clock pulses generated by the clocking system such that the sampling of the response signal is synchronized with the generation of the input signal and the curve fitting process minimizes the square of the deviation of the sampled response component from the known input signal and comprises mathematically fitting the response signal to the input signal to identify the background component the mathematical fitting process acting as a digital filter to reduce the effect of the background component in determining the dynamic characteristic of the system under test and wherein the DC offset is obtained by taking the average value of the response signal over a complete cycle. 
     
     
       20. The method as claimed in  claim 10 , further comprising feeding back of the response signal for use in calibrating the input signal wherein the feedback is used to:
 a) adjust the amplitude of the input signal to maintain operation of the measurement system and the system under test within a linear range; 
 b) adjust the gain and offset of the input signal to produce a response signal of near maximum amplitude and minimum offset without clipping of the response signal; and or; 
 c) provides compensation for errors introduced by the spectral phase and gain response of any one or more of amplifiers, ADCs and other circuitry in the system.